if tan(theta) = 1/2, find sin(theta) using trig identities

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if tan(theta) = 1/2, find sin(theta) using trig identities

"If tan(theta) = 1/2, find sin(theta) using trig identities."

I know how to do this with triangles: use pyth. thm to find the hypotenuse, and read off the answer. But what identity should I use?

little_dragon
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Re: if tan(theta) = 1/2, find sin(theta) using trig identities

I don't know identities but I've learned sin^2(@)+cos^2(@)=1. Try doing the tagent with sines and cosines.

tan(@) = 1/2 = sin(@)/cos(@)

Square both sides, and multiply acorss to get cos^2(@) = 4sin^2(@). Then add a sine to both sides to get cos^2(@)+sin^2(@)=5sin^2(@)=1. Then sin^2(@)=1/5. Do the square roots to get the answer.

anonmeans
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Re: if tan(theta) = 1/2, find sin(theta) using trig identities

I don't know what identities you have? The way the other post gave might be as good as any. But if you have to use something else, you could do 1 + tan2(theta) = sec2(theta) = 1/cos2(theta) = 1/{1 - sin2(theta)}, and plug in that 1 + tan2(theta) = 5/4. The answer works out the same.

mathproject
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Re: if tan(theta) = 1/2, find sin(theta) using trig identities

draw a triangle of tan(theta) = 1/2
once the triangle is drawn, use the pathagorean theorem (a² + b² = c²) to find the hypotenuse.
after all sides of the triangle are found, use SohCahToa to find sin(theta).

beachgirl6
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Re: if tan(theta) = 1/2, find sin(theta) using trig identities

First you should draw a right triangle and label the hypotenuse X and then the opposite side 1 and the adjacent side 2. That is what is known. Then by doing the Pythagorean theorem 1 squared plus 2 squared equals X squared. That will give you the X value. Then Sin theta will equal 1 over X.